Motion Of An Insect In The Rough Bowl MCQ - Practice Questions with Answers

Till the component of its weight along with the bowl is balanced by limiting frictional force, then only the insect crawls up the bowl, up to a certain height h  

         Let m=mass of the insect, r=radius of the bowl, μ= coefficient of friction for limiting condition at point A

$
R=m g \cos \theta \quad \ldots \ldots\left(\text { i) } \quad \text { and } \quad F_l=m g \sin \theta \quad \ldots \ldots\right.
$

Dividing (ii) by (i)

$
\begin{aligned}
& \quad \tan \theta=\frac{F_7}{R}=\mu \quad\left[\text { using } F_l=\mu R\right] \\
& \therefore \quad \frac{\sqrt{r^2-y^2}}{y}=\mu \quad \text { or } y=\frac{r}{\sqrt{1+\mu^2}} \\
& \text { So } \quad h=r-y=r\left[1-\frac{1}{\sqrt{1+\mu^2}}\right], \therefore h=r\left[1-\frac{1}{\sqrt{1+\mu^2}}\right]
\end{aligned}
$
 

where 

h = height up to which insect can climb

m = mass of insect

r = radius of the bowl

$\mu=$ coefficient of friction